$2.$ A spring is slowly compressed by a varying force $\backslash ($ F $\backslash )$ until it reaches an equilibrium state. Assuming that the force on the spring is proportional to the spring displacement, determine the work done on the spring. Assume that the constant of proportionality $\backslash ($ k $\backslash )$ is constant and expressed in pounds force per foot of spring deflection or newtons per meter of spring deflection. If a spring has a spring constant $\backslash ($ k $\backslash )$ of $\backslash (100\backslash$mathrm$\{$lbf$\}/\backslash$mathrm$\{$in$\}\backslash ).$ deflection. How much work is done when the spring is compressed $2$ in$.?$